Question

construct an angles with measure of degree 105 with the help of pair of compass and straight edge.write steps of construction

Answer 1

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how to draw 105 and 135 degrees with compass?  

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EXPERT ANSWERS

GSARORA17 | CERTIFIED EDUCATOR

1. Construction of angle 105 degree using compass:(Refer attached image)

Steps:

Draw a line AB and mark point O on it where angle is to be drawn.

With O as center draw an arc (semicircle) which intersects the line AB at points H and I.

Keeping the same radius as above and H as center, draw an arc which intersects the semicircle at point C. Without changing the radius as above and C as center, draw an arc which intersects the semicircle at point D. (The points C and D correspond to 60 and 120 degrees angle respectively).

Now draw two arcs of same radius keeping the centers as C and D respectively which intersect at point E.

Join points E and O and extend it to point X.

We get the angle XOB=90 degree.

Join the points O and D and extend it to point Y, so we get angle YOB=120 degree.

Angle YOX=Angle YOB-Angle XOB=120-90=30 degree

Now let’s bisect the angle YOX.

Draw two arcs of same radius keeping the centers D and F (point of intersection of EO and semicircle) which intersect at point G. Join GO.

We get the angle GOB=105 degree.

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Answer 2

step 1st: draw a line segment of 6cm. name 1st end point as A and 2nd as B.
step 2nd: draw a right angle.
now, add 15 degrees in it and name
it as C .thus,you get angle of 105
degrees